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The Study and Application of Baroclinic Ertel-Rossby Invariant in Meiyu Front Precipitation Process
斜压Ertel-Rossby不变量在梅雨锋降水过程中的研究与应用

GAO Shouting,LIANG Shengjun,DENG Difei,Lin Qing,
高守亭
,梁生俊,邓涤菲,林青

气候与环境研究 , 2012,
Abstract: In adiabatic and frictionless flow,Potential Vorticity(PV),characterized by its features of conservation,impermeability,and inversion,is widely used in diagnosis and analysis of the weather system over middle-high latitude.Due to its limitations of excluding the term of solenoid and of incapable of describing "fast-manifold" severe weather system,baroclinic Ertel-Rossby Invariant(ERI) proposed by Zdunkowski and Bott(2003) is analyzed and applied.The results show that under the condition of adiabatic and frictionless atmosphere,the expression of ERI includes the helicity,PV,and solenoid,and it can depict the "fast-manifold" systems,which make it possess huge potential practical value.Furthermore,the authors invoke ERI to diagnose a Meiyu front precipitation process from 3 Jul to 6 Jul 2003.The experiment reveals that the minimum of ERI coincides well with the 24-h accumulated rain band.Compared to PV,ERI is much capable in depicting and diagnosing the rainfall areas and rainfall amount.
“快流形”湿斜压Ertel-Rossby不变量的导出及其在台风中的应用  [PDF]
杨帅,高守亭,陈斌
中国科学 地球科学 中国科学 地球科学 , 2013,
Abstract: ?位涡因在绝热无摩擦大气中具有守恒性而被当作一个较好的示踪物广泛的应用.然而位涡本身,对于大尺度“慢流形”更为有效.因此,需要寻找另外的守恒的不变量来描述速度和气压场等快速变化的强天气过程,比如增长期和成熟的热带气旋.本文将湿大气中的焓和熵引入绝对运动方程来消除气压梯度项,并利用Weber变换和Ertel形式的连续方程,推导了湿大气中的斜压Ertel-Rossby不变量,并证明了其守恒性.推得的湿斜压Ertel-Rossby不变量的表达式除了包含传统的位涡项,它还包括气压梯度、位能和动能梯度项等能反映“快流形”特征的因子,以及干Ertel-Rossby不变量所没有的湿度因子,因此能更完善地描述湿过程中强天气现象快速变化的动力学特征.通过个例分析,与湿位涡和干大气中的Ertel-Rossby不变量相比,这个守恒的不变量对于台风这类真实湿大气中快速变化的强天气过程是一个较好的诊断分析工具,能表征几个共存台风组成的多台风系统的移动和强度变化.湿Ertel-Rossby不变量在真实湿大气中有较为广泛的应用前景.
广义ertel-rossby不变量在北京“7.21”暴雨过程分析中的应用  [PDF]
周玉淑,李娜,孙明生
气候与环境研究 , 2014, DOI: 10.3878/j.issn.1006-9585.2013.13010
Abstract: 在绝热无摩擦大气中,具有守恒性及可反演性的ertel位涡(pv)在大尺度天气系统分析中有广泛应用。由于忽略了力管项的作用,pv用于分析中小尺度天气系统演变时受到局限。从广义速度推导得到的广义ertel-rossby不变量(geri)除了包含有pv的守恒性,还包含了螺旋度效应及力管项的作用,对于分析研究快变流型的中小尺度系统演变有一定优势。用geri分析2012年7月21日北京地区的特大暴雨过程,表明geri在暴雨区有明显的异常出现,其异常基本与暴雨出现时间同位相,表明geri的定义涵盖了螺旋度和pv,也包含了暴雨发生时的旋转斜压大气的力管项效应,确实能体现暴雨过程中的流型快变的特点,可以作为独立的变量来分析和揭示造成暴雨的低涡系统的动力结构,为诊断和预报暴雨落区提供新的动力物理量。
Relativistic least action principle for discontinuous hydrodynamic flows, Hamiltonian variables, helicity and Ertel invariant  [PDF]
A. V. Kats
Physics , 2004,
Abstract: A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of breaks (including shocks) is presented in the framework of an exact Clebsch type representation of the four-velocity field as a bilinear combination of the scalar fields. The boundary conditions for these fields on the breaks are found. We also discuss the local invariants caused by the symmetries of the problem, including relabeling symmetry. In particular, the generalization of the well-known nonrelativistic Ertel invariant is presented.
斜压ertel-rossby不变量在梅雨锋降水过程中的研究与应用  [PDF]
高守亭,梁生俊,邓涤菲,林青
气候与环境研究 , 2012, DOI: 10.3878/j.issn.1006-9585.2011.10143
Abstract: 绝热无摩擦下,位涡(pv)的守恒性、不可渗透性和可反演性使之非常广泛地应用在中高纬度天气学诊断分析中,但由于其本身不包含力管项,无法描述强烈天气的快速流形等局限性,因此分析了zdunkowskiandbott(2003)提出的斜压ertrl-rossby不变量(eri),结果表明,绝热无摩擦条件下的eri在其表达式中就已经明确地包含了螺旋度和pv的表达式,同时也涵盖了斜压大气中的力管项效应,可以描述快速流形的天气系统,具有pv所不能取代的优点,这使得它具有非常广泛的潜在应用价值。在此基础上,还利用eri诊断了2003年7月3~6日的一次梅雨降水过程,结果表明,eri完整地刻画了这次降水带南移及降水强度变化的特点,随着24h累积降水带的移动,eri低值区也随之移动,二者吻合非常好。和pv相比,eri对降水落区及强度变化的诊断能力更强。
On the generalized Futaki invariant  [PDF]
Mirroslav Yotov
Mathematics , 1999,
Abstract: We study the algebraic properties of the generalized Futaki invariant of an almost Fano variety and prove that it is in fact a pushforward to a point of an appropriate equivariant Chow cohomology class of the variety. This allows us to use Bott-type formulae for calculating the invariant. We show this use on some examples.
Group invariant Colombeau generalized functions  [PDF]
Hans Vernaeve
Mathematics , 2005,
Abstract: Colombeau generalized functions invariant under smooth (additive) one-parameter groups are characterized. This characterization is applied to generalized functions invariant under orthogonal groups of arbitrary signature, such as groups of rotations or the Lorentz group. Further, a one-dimensional Colombeau generalized function with two (real) periods is shown to be a generalized constant, when the ratio of the periods is an algebraic nonrational number. Finally, a nonstandard Colombeau generalized function invariant under standard translations is shown to be constant.
Generalized Invariant Monotonicity and Generalized Invexity of Nondifferentiable Functions
Liu Caiping,Yang Xinmin
Journal of Inequalities and Applications , 2009,
Abstract: New concepts of generalized invex functions for non-differentiable functions and generalized invariant monotone operators for set-valued mappings are introduced. The relationships between generalized invexity of functions and generalized invariant monotonicity of the corresponding Clarke's subdifferentials are studied. Some of our results are extension and improvement of some results obtained in (Jabarootion and Zafarani (2006); Behera et al. (2008)).
Generalized (ρ,θ)-η Invariant Monotonicity and Generalized (ρ,θ)-η Invexity of Nondifferentiable Functions
Caiping Liu,Xinmin Yang
Journal of Inequalities and Applications , 2009, DOI: 10.1155/2009/393940
Abstract: New concepts of generalized (ρ,θ)-η invex functions for non-differentiable functions and generalized (ρ,θ)-η invariant monotone operators for set-valued mappings are introduced. The relationships between generalized (ρ,θ)-η invexity of functions and generalized (ρ,θ)-η invariant monotonicity of the corresponding Clarke's subdifferentials are studied. Some of our results are extension and improvement of some results obtained in (Jabarootion and Zafarani (2006); Behera et al. (2008)).
Rossby wave propagation tracks in southern hemisphere mean basic flows associated to generalized frosts over southern South America
MüLLER, G. V.;AMBRIZZI, T.;
Atmósfera , 2010,
Abstract: based on previous observational studies on cold extreme events over southern south america, some recent studies suggest a possible relationship between rossby wave propagation remotely triggered and the occurrence of frost. using the concept of linear theory of rossby wave propagation, this paper analyzes the propagation of such waves in two different basic states that correspond to austral winters with maximum and minimum generalized frost frequency of occurrence in the wet pampa (central-northwest argentina). in order to determine the wave trajectories, the ray tracing technique is used in this study. some theoretical discussion about this technique is also presented. the analysis of the basic state, from a theoretical point of view and based on the calculation of ray tracings, corroborates that remotely excited rossby waves is the mechanism that favors the maximum occurrence of generalized frosts. the basic state in which the waves propagate is what conditions the places where they are excited. the rossby waves are excited in determined places of the atmosphere, propagating towards south america along the jet streams that act as wave guides, favoring the generation of generalized frosts. in summary, this paper presents an overview of the ray tracing technique and how it can be used to investigate an important synoptic event, such as frost in a specific region, and its relationship with the propagation of large scale planetary waves.
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